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My question is , will the wave function collapse because any energy passing through the void , may be conserved by the void ?
Quote from: Armad on 03/06/2022 13:43:25My question is , will the wave function collapse because any energy passing through the void , may be conserved by the void ? What wave function, please specify. Also specify what measurement is being made.If volume 2 is a void, why bother with a void between the 2 volumes.
The wave function can be any carrier signal or natural wave function of electromagnetic radiation . The measurements of volume one can be viewed as an Eigenstate or the vacuum physical constants . The measure of volume two is absolute 0 . A void between the volumes just made it easier to show the question , allowing a vector x for discussion purposes if required .
Quote from: Armad on 03/06/2022 14:17:08The wave function can be any carrier signal or natural wave function of electromagnetic radiation . The measurements of volume one can be viewed as an Eigenstate or the vacuum physical constants . The measure of volume two is absolute 0 . A void between the volumes just made it easier to show the question , allowing a vector x for discussion purposes if required . We all know what Hilbert spaces are, but your “useful note” does not help understand the quote above.What are you actually measuring and what is the vector x.Try to be specific rather than making up meaningless phrases, otherwise I’ll start calling you Steve!
I have no idea why you would move a thought experiment with a question to new theories when it isn't a new theory ?
title of the thread asks a question , ''In this thought experiment would the wave function ''collapse'' ?
My conclusion to my own question was that when unbounded electromagnetic radiation travels from within the Hilbert space , arriving at the ''border'' between Hilbert space and spaces that may be infinite-dimensional, that the wave function collapses based on the attached equation .
Quote from: Armad on 03/06/2022 14:52:15I have no idea why you would move a thought experiment with a question to new theories when it isn't a new theory ?It certainly seems like a new theory.Quote from: Armad on 03/06/2022 14:52:15title of the thread asks a question , ''In this thought experiment would the wave function ''collapse'' ?OK, the answer is no, mainly because there is no wave function specified so there is nothing to collapse.
Quote from: Armad on 03/06/2022 15:34:25My conclusion to my own question was that when unbounded electromagnetic radiation travels from within the Hilbert space , arriving at the ''border'' between Hilbert space and spaces that may be infinite-dimensional, that the wave function collapses based on the attached equation . There's no such thing as an infinite-dimensional space, so there is no border so the question is moot.
I do not see your argument , wave function in general can be specified Ψ without a specific value .
This question would apply to all energies that have motion .
A particle travelling outwards from within the Hilbert space frame of reference would also be stoppable at the ''border'' of Hilbert space . The ''border'' of Hilbert space could be viewed as an impenetrable wall that isn't constructed of matter or energy .
''In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. A Hilbert space is a vector space equipped with an inner product which defines a distance function for which it is a complete metric space. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces.''
Quote from: Armad on 03/06/2022 15:56:41I do not see your argument , wave function in general can be specified Ψ without a specific value .That is not the problem, you stated, "would the wave function collapse?" What wave function? Quote from: Armad on 03/06/2022 15:56:41This question would apply to all energies that have motion .This is difficult to answer since that really doesn't make sense as stated. I assume you are talking about a photon for instance, which is not energy but carries energy.Quote from: Armad on 03/06/2022 15:56:41A particle travelling outwards from within the Hilbert space frame of reference would also be stoppable at the ''border'' of Hilbert space . The ''border'' of Hilbert space could be viewed as an impenetrable wall that isn't constructed of matter or energy .Well obviously if the wall was impenetrable the particle would stop. This 'border' however, is not something that would occur in the real world it is more in the realm of science fiction.
Is the conservation of energy science fiction ?
When a photon travels at the speed of light and reaches the Hilbert spaces '''border'' , the wave-function collapse could be viewed as : E=mc²
Quote from: Armad on 03/06/2022 15:59:51''In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. A Hilbert space is a vector space equipped with an inner product which defines a distance function for which it is a complete metric space. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces.''No, I am saying you do not understand this. You need to understand the basics of physics before trying to tackle more complicated topics.
The wave function can be any carrier signal or natural wave function of electromagnetic radiation .
In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. A Hilbert space is a vector space equipped with an inner product which defines a distance function for which it is a complete metric space. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces.''
Quote from: Armad on 03/06/2022 16:36:46Is the conservation of energy science fiction ?No.Quote from: Armad on 03/06/2022 16:36:46When a photon travels at the speed of light and reaches the Hilbert spaces '''border'' , the wave-function collapse could be viewed as : E=mc²You keep talking about this border between a mathematical concept and spacetime, how does that make any sense?
Hi. 1. I would have asked a similar question to Colin2B about your original post: Usually we don't consider there to be one wave function to describe everything. Typically each particle has its own wave function and depending on the set up of your experiment or theoretical situation, it can be possible to make an observation that will collapse one wave function but not the other. In Quantum Field Theory you get a bit closer to there being one wave function for everything. Every particle of the same type shares one field, for example an electron is always an oscillation in the same electron field. However, there are are still many fields, one for each particle in the standard model. So, when you asked about "the" wave function as if there is only one to describe everything, then that has moved the discussion to the edge of currently established and mainstream science. There may be one wave function to describe everything but that's not well established at the moment.2. Quote from: Armad on 03/06/2022 14:17:08The wave function can be any carrier signal or natural wave function of electromagnetic radiation . That's also not a conventional description of what a wave function is.Quote from: Armad on 03/06/2022 14:52:15I have no idea why you would move a thought experiment with a question to new theories when it isn't a new theory ? Maybe @Colin2B made a mistake but you can see why they weren't sure.3. About Hilbert Spaces:Quote from: Armad on 03/06/2022 15:59:51In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. A Hilbert space is a vector space equipped with an inner product which defines a distance function for which it is a complete metric space. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces.'' That quote seems OK. However, I think the problem is that the word "space" appears in the title "Hilbert Space" and you are assuming it must have something to do with real physical space out in the universe. A Hilbert space is a very general algebraic object and the elements in this space are not usually points (or vectors) in our physical space. In conventional Quantum Mechanics, the elements of our Hilbert space are the wave functions. This is complicated and not worth trying to explain in a forum post. There are texts written on the subject but they aren't short. The main point is that Hilbert Space isn't used to describe a location in actual physical space, or even to describe the behaviour and properties of a region of actual space. Instead it usefully describes how we can combine and manipulate wave functions. So things don't move "out of the Hilbert Space" and into some other space, it's just not a description of location or of space.Can I answer the question? Not really and I'm sorry about that. I can't easily connect what is being asked with what little Physics is known to me. I don't think I can help much.Best Wishes.
A mathematical concept that represents a physical concept . Space-time is a mathematical model , you could measure a Hilbert space using space-time .
Quote from: Armad on 03/06/2022 16:51:34A mathematical concept that represents a physical concept . Space-time is a mathematical model , you could measure a Hilbert space using space-time .You're not getting this. In mathematics we set up boundary condition. Lets say I want to know the number of gamma rays in a cubic meter that is 10 meters from a gamma ray source. If I know the dimensions of the source and the radioactive isotope I can calculate the number of gamma rays passing through that enclosed boundary per second. You are asking the question, "what happens to the gamma rays when they hit the boundary?" The answer is, they never hit the boundary because it is a mathematical concept not an actual boundary!